Possible model theoretic semantics for equivalentTo

From: Jeff Heflin ([email protected])
Date: 01/16/01 

Just off the top of my head, what if we modified the model-theoretic
semantics so that:

<equivalentTo, ?O, ?P>		IO(?O) = IO(?P)
<sameClassAs, ?C, ?D>		IO(?C) = IO(?D) and IC(?C) = IC(?D)
<samePropertyAs, ?R, ?S>	IO(?R) = IO(?S) and IR(?R) = IR(?S)

This would say that equivalentTo establishes equivalence between
resources, with subproperties that specify additional meaning for
resources that are classes and properties. This fits with RDF's notion
that classes and properties are also elements of your domain of
discourse, while preserving the notion of sameClassAs and samePropertyAs
being subproperties of equivalentTo.

One potential flaw in these semantics is that <equivalentTo,X,Y> where X
and Y are classes does not mean the same thing as <sameClassAs,X,Y>. If
there were subsets of DD, lets say Classes and Props, that identify
which individuals are classes and which are properties, then maybe we
could say something like:

<equivalentTo, ?O, ?P>		IO(?O) = IO(?P),
				if ?O and ?P in Classes then IC(?O)=IC(?P)
				if ?O and ?P in Props then IR(?O)=IR(?P)

or alternatively, we could simply add the following general rules to our
semantics:

IO(?C) = IO(?D) and ?C,?D in Classes iff IC(?C) = IC(?D)
IO(?R) = IO(?S) and ?R,?S in Props iff IR(?R) = IR(?S)

Jeff

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